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Properties

Label 12.5.d
Level $12$
Weight $5$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $10$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(12, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\( 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9} + O(q^{10}) \) \( 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9} - 172 q^{10} + 180 q^{12} + 296 q^{13} + 600 q^{14} + 112 q^{16} - 600 q^{17} - 162 q^{18} - 1368 q^{20} - 144 q^{21} - 1128 q^{22} + 1296 q^{24} + 972 q^{25} + 1692 q^{26} + 1488 q^{28} + 888 q^{29} - 1980 q^{30} - 2784 q^{32} + 720 q^{33} - 484 q^{34} + 540 q^{36} - 4408 q^{37} + 4680 q^{38} + 1664 q^{40} + 552 q^{41} - 2088 q^{42} - 3696 q^{44} - 648 q^{45} - 384 q^{46} + 1008 q^{48} - 572 q^{49} - 1038 q^{50} + 6008 q^{52} + 5112 q^{53} + 486 q^{54} + 1728 q^{56} + 5616 q^{57} - 124 q^{58} - 2664 q^{60} + 4232 q^{61} - 7224 q^{62} - 14720 q^{64} - 18192 q^{65} + 4824 q^{66} + 5496 q^{68} - 9792 q^{69} + 6096 q^{70} + 8840 q^{73} - 4116 q^{74} - 1872 q^{76} + 20928 q^{77} + 9900 q^{78} + 25632 q^{80} + 2916 q^{81} + 3740 q^{82} - 10512 q^{84} - 10256 q^{85} - 19560 q^{86} - 8640 q^{88} - 25080 q^{89} + 4644 q^{90} + 18816 q^{92} - 17136 q^{93} - 5232 q^{94} - 8352 q^{96} + 23048 q^{97} - 5850 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.5.d.a 12.d 4.b $4$ $1.240$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(6\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)